# Beta of FTSE100 stocks against benchmark index FTSE100

first post so if I write something silly don't hold it against me.

I calculated beta for almost all the stocks that compose the FTSE100. All have beta < 1. This, as far as I understand it, means that they are all less volatile than the benchmark index.

But, how can it be? Shouldn't some of the stocks that compose the index be more volatile??

--EDIT--

I downloaded 1 year long historical data for FTSE100 and for several stocks.

I calculated the daily movements (% returns) with the formula:

(close_price_today - close_price_yesterday) /close_price_yesterday


for each day except the last naturally. Did the same for both FTSE100 and all the stocks.

Then used slope function using FTSE100 using:

=SLOPE(array%ret_stock , array%ret_FTSE100)


the values are all above 0 and all below 1 (highest is approximately 0.6)

Here is a sample of what I did: https://docs.zoho.com/file/egrja03b89e74f3ca4dac91e8a02b0d950156

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I think there's something wrong. Could your post more information? How did you calculate your betas? – pincopallino Jun 17 '14 at 14:17
It is not true that small beta means low vol. There is still idiosyncratic risk in the stocks. – Richard Jun 18 '14 at 10:58
I said less volatile then the benchmark index. Relatively to an index the stock/portfolio with low beta is supposed to be less volatile than one with a higher beta. Is this not correct? – Alvin Jun 18 '14 at 11:12

Beta is calculated as Rstock = alpha + beta*Rindex. When you use slope in excel the first value is for the y's so you are doing it wrong, you should have slope(Stock returns, Index returns). While that is the formula you use above it is not the one in the excel, with the data you provide I get a beta of 0.96.

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I will try to recalculate it for all the stocks in FTSE100 and update this question. Thank you. – Alvin Jun 18 '14 at 11:03
Now the values seem to have more sense, as some of them are more volatile then the market and some less as shown in this subset: docs.zoho.com/file/egrjaad494fbcf4f34c0f9807fef68dd8fd95 I guess the order of x_data and y_data in the spreadsheet confused me a bit.. – Alvin Jun 18 '14 at 13:48
Awesome, it seems fine now. Just one small note, as previously said, be careful by saying a lower beta implies lower volatility because stocks also have idyonsicratic risk. The lower beta - lower volatility argument holds only if you are adding the stock to a well diversified portfolio because the specific risk is diversified away. – Artur Silva Jun 18 '14 at 15:38

The computation of Beta is rather simple. Please try using my following procedures:

$$ret_i = ret_{i} - ret_{rf}$$ $$ret_b = ret_{benchmark} - ret_{rf}$$ then $$\beta_{i} = \frac{cov(ret_p, ret_b)}{var(ret_b)}$$

where $ret_b$ is the benchmark return net of risk-free rate, $ret_i$ is the stock return net of risk-free rate, $cov$ is the covariance operator and $var$ is the variance operator. $\beta_{i}$ is the beta of the $i_{th}$ stock in the portfolio.

In this case benchmark return is FTSE100 Index, and stock return is the return of a given component stock in this universe. And risk-free rate can be taken as 0 given the low-interest environment of developed markets.

Generally low beta stocks are less volatile than high beta stocks. Usually large cap stocks tend to have lower beta than small-cap stocks. Beta can be used as a proxy for volatility and riskiness of a security, although they are not equivalent.

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Thank you for the explanation. I solved the problem few days ago. I was using the data in the wrong order. Can you briefly explain more on the difference between volatility and riskiness? (Or just point me to a source where I can learn more?) – Alvin Jun 25 '14 at 13:06
Hi Alvin: they are different concept. Volatility is a double-edged sword, and it does not essentially measure the risk a traditional investor perceives. In a rising market, high volatility leads to higher return potential, as volatility (measured as standard deviation) does not differentiate between upside and downside dispersion. You may find this helpful. – Simon Jun 25 '14 at 13:15